Asymptotics for L2 minimal blow-up solutions of critical nonlinear Schrödinger equation

Abstract

In this note, we describe the behavior of a sequence $v_n:R^N\to C$ minimal in $L^2$ such that $\frac{1}{2}\int {\left|\nabla v_n\right|}^2-\frac{1}{\frac{4}{N}+2}\int {\left|v_n\right|}^{\frac{4}{N}+2}\le E_0$ and ${\left|v_n\right|}_{H^1}\to +\infty$.

Résumé

Dans cette note, on explicite de façon optimale le comportement d'une suite $v_n:R^N\to C$ de norme $L^2$ minimale telle que $\frac{1}{2}\int {\left|\nabla v_n\right|}^2-\frac{1}{\frac{4}{N}+2}\int {\left|v_n\right|}^{\frac{4}{N}+2}\le E_0$ et ${\left|v_n\right|}_{H^1}\to +\infty$.